Local anchor for group master (move/translate/offset of group master moves group instances)?
Creating a group-instance is a different thing from creating a linked duplicate.
When you create a linked duplicate, the object data is shared between the two objects, but each object can be transformed or changed with modifiers without affecting the other.
 
group instances, on the other hand inherit all of the geometry and data characteristics of their defining group of objects and also inherit their transforms with respect to the scene origin, not the group objects center.
The empty of the group instance acts as an additional displacement gizmo so that you can transform the instance, but moving the parent objects in the global coordinate system will propagate that change to the group instances.

Unfortunately, there's no such thing as a group origin-even a temporary one, so you can't produce a group instance that doesn't behave this way.  Programs like AutoCAD have what are called 'blocks' which are collections of entities with a local coordinate system so that you can instance and transform them.  AutoCAD stores block data in a non-graphical part of its and replaces the defining geoemtry with an instance of the block.

You acheive this same effect in blender by creating a group in a seperate blend file and then instancing it in your scene.
It's not always convenient to have a file link between a group definition and an instance of the group, so what I've generally done is assign my grouped objects to a layer that's turned off or create them in a new scene and then use instances everywhere in the layout scene.